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Mathematics - Secondary Curriculum Secondary Mathematics I
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Strand: FUNCTIONS - Interpreting Linear and Exponential Functions (F.IF)

Understand the concept of a linear or exponential function and use function notation. Recognize arithmetic and geometric sequences as examples of linear and exponential functions (Standards F.IF.13). Interpret linear or exponential functions that arise in applications in terms of a context (Standards F.IF.46). Analyze linear or exponential functions using different representations (Standards F.IF.7, 9).

Standard F.IF.1

Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

  • Derivate
    Students may use the applet in this lesson to graph a function and a tangent line and view its equation.
  • Do two points always determine a linear function?
    This problem allows the student to think geometrically about lines and then relate this geometry to linear functions. Or the student can work algebraically with equations in order to find the explicit equation of the line through two points (when that line is not vertical).
  • Domain and Range
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Domains
    The purpose of this task to help students think about an expression for a function as built up out of simple operations on the variable, and understand the domain in terms of values for which each operation is invalid (e.g., dividing by zero or taking the square root of a negative number).
  • Finding the domain
    The purpose of this task is to introduce the idea of the domain of a function by linking it to the evaluation of an expression defining the function.
  • Function Flyer
    The applet on this site allows the students to manipulate the graph of a function by changing the value of exponents, coefficients and constants.
  • FUNCTIONS - Interpreting Linear and Exponential Functions (F.IF) - Sec Math I Core Guide
    The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for the Secondary Mathematics I Interpreting Linear and Exponential Functions (F.IF).
  • Interpreting the Graph
    Students will use the graph (for example, by marking specific points) to illustrate the statements in (a) and (d). If possible, label the coordinates of any points you draw.
  • Introduction to the Materials (Math 1)
    Introduction to the Materials in the Mathematics One of the The MVP classroom experience begins by confronting students with an engaging task and then invites them to grapple with solving it. As students ideas emerge, take form, and are shared, the teacher orchestrates the student discussions and explorations towards a focused mathematical goal. As conjectures are made and explored, they evolve into mathematical concepts that the community of learners begins to embrace as effective strategies for analyzing and solving problems.
  • Linear Functions
    The applet in this lesson allows students to manipulate variables and see the changes in the graphed line.
  • Module 3: Features of Functions - Student Edition (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 3, Features of Functions, is the culminating functions module in Secondary Math I. In this module, students broaden their thinking about functions to relationships that are not either linear or exponential.
  • Module 3: Features of Functions - Teacher Notes (Math 1)
    The Mathematics Vision Project, Secondary Math One Module 3 Teacher Notes, Features of Functions, is the culminating functions module in Secondary Math I. In this module, students broaden their thinking about functions to relationships that are not either linear or exponential.
  • Points on a Graph
    This task is designed to get at a common student confusion between the independent and dependent variables. This confusion often arises in situations like (b), where students are asked to solve an equation involving a function, and confuse that operation with evaluating the function.
  • Representing Functions and Relations
    This collection of resources to teach graphing equations in slope intercept form includes warm-up exercises, a video presentation explaining the topic, practice exercises, worked examples, practice problems, and a review.
  • Representing Functions and Relations video
    Explains how algebra can be used to describe, represent and predict relations.
  • Sequencer
    By using this applet students are able to create sequences by changing the values of starting numbers, multipliers, and add-ons.
  • The Customers
    The purpose of this task is to introduce or reinforce the concept of a function, especially in a context where the function is not given by an explicit algebraic representation. Further, the last part of the task emphasizes the significance of one variable being a function of another variable in an immediately relevant real-life context. Instructors might prepare themselves for variations on the problems that the students might wander into (e.g., whether one person could have two home phone numbers) and how such variants affect the correct responses.
  • The Parking Lot
    The purpose of this task is to investigate the meaning of the definition of function in a real-world context where the question of whether there is more than one output for a given input arises naturally. In more advanced courses this task could be used to investigate the question of whether a function has an inverse.
  • Using Function Notation I
    This task deals with a student error that may occur while students are completing F-IF Average Cost.
  • Vertical Line Test
    This interactive applet asks the student to connect points on a plane in order to build a function and then test it to see if it's valid.
  • Your Father
    This is a simple task touching on two key points of functions. First, there is the idea that not all functions have real numbers as domain and range values. Second, the task addresses the issue of when a function admits an inverse, and the process of "restricting the domain" in order to achieve an invertible function.


UEN logo http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.